A305394 First differences of A140103.

5, 4, 5, 3, 5, 4, 5, 5, 4, 5, 3, 5, 4, 5, 4, 5, 3, 5, 4, 5, 5, 4, 5, 3, 5, 4, 5, 3, 5, 4, 5, 5, 4, 5, 3, 5, 4, 5, 4, 5, 3, 5, 4, 5, 5, 4, 5, 3, 5, 4, 5, 5, 4, 5, 3, 5, 4, 5, 4, 5, 3, 5, 4, 5, 5, 4, 5, 3, 5, 4, 5, 3, 5, 4, 5, 5, 4, 5, 3, 5, 4, 5, 4, 5, 3, 5, 4, 5, 5, 4, 5, 3, 5, 4, 5, 4

Offset

1,1

Comments

Conjecture: this sequence is the ternary tribonacci word on the alphabet {5,4,3}, i.e., (a(n)) is the unique fixed point of the morphism 5 -> 54, 4 -> 53, 3 -> 5; see A092782. - Michel Dekking, Mar 13 2019

An equivalent conjecture: This sequence (prefixed by 3 since A140103 should really begin with 0) is 3.TTW(5,4,3) where TTW is the ternary tribonacci word defined in A080843, or equally it is THETA(5,4,3), where THETA is defined in A275925. There are similar conjectures for the first differences of A140100, A140101, A140102. - N. J. A. Sloane, Mar 14 2019 and Mar 19 2019

All these conjectures are now theorems - see the Dekking et al. paper. - N. J. A. Sloane, Jul 22 2019

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..49999F.

Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

Formula

a(n) = A140103(n+1) - A140103(n).

Crossrefs

For first differences of A140100, A140101, A140102, A140103 see A305392, A305374, A305393, A305394.

Sequence in context: A160789 A266111 A131291 * A361803 A344124 A237577

Adjacent sequences: A305391 A305392 A305393 * A305395 A305396 A305397

Keyword

nonn

Author

N. J. A. Sloane, Jun 23 2018

Status

approved